The Soviet statistician, V V Natimov, has recently completed a trilogy of which the third volume (160) constitutes a remarkable synthesis drawing on the entire range of knowledge (including elements of semantics, natural and social sciences, mysticism, and the arts) in an effort to understand how the human mind perceives the world. The methodology is borrowed largely from physics (as capable of tolerating paradoxes within its own theories), with considerable attention to the role of metaphor and the function of human imagination in capturing manifestations of consciousness and unconsciousness. The primary ontological position is that the world is an open one, the outcome of processes that are probabilistic in nature and constantly the domain of novelties and uncertainties. The language in which one captures aspects of Reality is itself polymorphic, metaphorical, and constrained_by Godelian principles of undecidability. Right and left hemisphere modes of consciousness are, through links provided by the unconscious, capable of functioning along unusual circuits so that sequential processes become concurrent in real time.

For Nalimov the "words, on which our culture is based, do not and cannot have an atomistic meaning. It has become possible and even necessary to consider words as possessing fuzzy semantic fields over which the probabilistic distribution function is constructed and to consider people as probabilistic receivers" (160, pp. 5-6). This leads him to ask whether taxa are discrete, as is normally assumed in the various typologies through which the world is perceived, especially in connection with human and social development.

"What we are considering is not merely the probabilistic vision of the world stemming from its infinite complexity, but inwardly deterministic "in fact". We mean the probabilistic world where probability lies at the core of the world. We mean probabilistic ontology of the probabilistic world, not probabilistic epistemology of a deterministic world" (160, p. 6)

Acquaintance with taxonomy in various branches of knowledge leads him to suggest the hypothesis that "taxa probabilistic by nature are neither an exception to nor a result of deficiency in our cognition; they are the rule and an immanent property of the world." (160, p. 7) Consequently in the probabilistic world clear-cut boundaries and the absence of embarrassing "transitional forms" merely testify to a reduction in completeness.

"We are accustomed to the idea that evolution means the appearance of something absolutely new. The truly new thing is a new taxon or archetype. But within the world of probabilistic taxa, archetypes, and individuals, evolution may take another course: it suffices to redistribute probabilities. A rare deviation becomes the norm, while the norm becomes an abnormality, an atavism. 6ut potentiality still exists....What we keep in mind is the constant potentiality which underlies various probabilities of manifestation." (160, p. 8)

For Nalimov, culture is a deep collective consciousness whose roots lie in the remotest part. It forms a fuzzy mozaic of concepts with the distribution function of probabilities given over it. But real people have their own individual probabilistic filters of perception which generate personal perception of culture, again probabilistically given. The (Jungian) collective unconsciousness is then related to low probability concepts. Groups in society with similar filters then constitute clusters or psychic genotypes. In this probabilistic sense man is never free being dominated by the past as stored in the collective consciousness. But at the same time he is free because the genotype does not rigidly determine the probabilistic structure of an individual filter of perception; it only gives certain possibilities for its formation (160, p. 9)

Nalimov stresses the continuous nature of consciousness, with which a person is always in contact, but which cannot be reduced to the discreteness of language (except partially through rhythmical texts). Phrases constructed over discrete symbol-words are always interpreted at the continuous level. "The continuous nature of everyday language finds its expression in the limitless divisibility of the verbal meanings, while the continuous nature of the morphology of the animate world is expressed by the impossibility of constructing a discrete taxonomy." (160, p. 30)

This leads him to suggest that:

"Perhaps we should be more cautious and speak not of consciousness of the world but of the semantic field of universal significance through which the world we know as divided is restored in its wholeness. Is there any other way to imagine the world in its integrality?" (160, p. 14)

The question is then what is the semantic field of the world. "How can the fuzzy, probabilistically weighted vision of the world be combined with formal logic, which we cannot afford to reject?" (160, pp. 1 5). If one phenomenon can be explained by several scientific hypotheses, "there is still a tendency to evaluate these hypotheses and to select the only true one. If this cannot be done, the situation is evaluated as obviously unsatisfactory. Is it possible to act otherwise, i.e., to perceive the phenomenon through a field of hypotheses, without their discrimination...But shall we be able to cope with this at the psychological Ivel: is our rnind ready for this vision of the world?" (I 60, p. 1 6). And how is this field to be conceived as being organized for comprehension?

Nalimov suggests that: "If all the taxa of our culture, despite their uniqueness, are but various translations of our Text...and biological species are various translations of another Text, then it is quite plausible that they all are translations of one and the same Text." (160, p. 14). The world is then seen as a text, and through texts accessible to consciousness individuals interact with the world (160, p. 26). The question directly relevant to human and social development is how such texts evolve.

Transformative evolution, according to Nalimov, results from the multiplicative nature of the interaction between two probability distribution functions, one corresponding to the Initial text and the second to a preference filter. Then it is not the initial text but the filter which changes. Thus the progress of science also consists effectively of the endless filtration of new ideas through the filter of paradigmatic criteria carried by past conceptions - filters which may be softened, rather than destroyed, when they prove inadequate.

Innovative development can then be seen as a response to a semantic vacuum. "New texts are always a result of free creativity realized on a probabilistic set which may be regarded as an unexposed semantic universe or nothing, the semantic vacuum or, metaphorically, an analogue of the physical vacuum. Here we deal with the problem of nothing which stimulated thinkers both in the East...and in the West..." (160, p. 29)

Nalimov devotes three chapters to this question. Of special interest is his concept of the way a person is defined for himself and others both through the generation of discrete words or symbols and through their comprehension at a continuous level. Both aspects are realized through contact with the semantic field, which in physical terms can be described as emission and absorption of semantic field quanta. But in the light of the Heisenberg uncertainty relation, "semantic interaction between people...is possible only as a consequence of semantic fuzziness of both the human psychic domain and verbal semantics." (160, p. 76). Humans may however, interact with the semantic vacuum through unobservable (virtual) vacuum manifestations:

"Just as any physical virtual particles of various types, very similar processes go on in the psychic domain too. The latter may be described as a constant fluctuation of the probability distribution function determining a person's individuality on the semantic field. A human being never remains frozen and unchanged." (160, p. 77)

Nalimov then reviews experiments in meditation, some of which were conducted with his colleagues. In his terms such experiences

"may be reinterpreted as a ceaseless reconstruction of the distribution function of probabilities determining a person's individuality....The keen interest of modern Western man in meditation is easily understandable: the culture of our time has squeezed human individuality, and the distribution function determining personality is becoming needle-shaped. Meditation is a technique that allows people to loosen this unbearably narrow__structure, to make it fuzzy. (160, p. 138)

These considerations lead Nalimov to ask the question: "in what way can a possible change in the metrics of the semantic space be interpreted?" (160, p. 287). In the physical analogue changes of fundamental constants are thought to produce another physical world. He sees the entire past, through the colonial period, as involving an expansion of the life space. "In contrast, we see the new as an expansion of the space for human existence - the entrance into new psychological spaces. But is our consciousness mature enough not to pollute these new spaces?" (160, p. 300). Such new spaces also call for a multidimensional concept of personality which he explores (160, p. 287).

Of special interest in the light of the arguments of this paper is Nalimov's view that the Aristotelian bimodal logic cannot be replaced by another one:

"The insufficiency of logic in everyday language is made up for by the use of metaphors. The logic of the text and its metaphorical side are two mutually complementary phenomena. And, to my mind, further evolution of linguistic means should proceed by deepening language complementarity rather than by searching for another kind of logic." (160, p. 281).

According to the complementarity principle, in order to reproduce an object in its integrity it is necessary to alternate through a pattern of descriptions of it in terms of mutually exclusive classes of concepts. This implies the use of a "manifold of models generated by essentially different paradigms", but Nalimov questions " whether people are prepared for this intentionally incomplete vision of the world" (160, pp. 276 and 283). However, as has been argued earlier in this paper:

"If it is typical of human reason to perceive the world through antinomies, why not try to find a language in which these antinomies...would act as mutually complementary principles." (160, p. 284)

Nalimov points out that:

"Clear-but conceptualization oppositions create the polarization without which the passionate temperament of individuals that provides society with its energy could not have been realized" (160, p. 294). Such "passionarity" looks like an obsession and has dramatic consequences when expressed collectively. But without it, persons or nations may lose their energy. "We must acknowledge passionarity to be immanent to people. A selective manifestation of the whole, man tends to discover the entrance for the selectivity and thus acquires energy" (160, p. 295).

Again as argued in this paper, Nalimov sees the manifested semantic universe as structured not by logic, but by number (160, p. 285). In this sense he considers the probabilistic vision of the world to be a realization of the dream of Pythagoras and Plotinus of describing the world in its integrity and fuzziness through number, or through a "koan of numbers" (160, p. 32-36). But despite an extensive review of Eastern and Western symbols (including mandalas), he seems to limit his attention to numbers in their probabilistic sense rather than extending it to include their configurative geometrical sense, although Chladni patterns (164) might be considered a link between the two. Whereas this paper stresses the possibility of using number-governed configurations of complementary languages, symbols or metaphors to provide a variety of learner-responsive ways of organizing comprehension of the semantic universe and the possibilities of acting in it.

In the light of Nalimov's work it is possible to imagine configurations of complementary languages as being organized as N-dimensional "semantic Chladni patterns". These would probably only be comprehensible where N was less than 4. Clearly when N was 2, these could resemble many of the symbols discussed by Nalimov. With N equal to 2 or 3, they might resemble the "macrons" examined by Ralph Abraham (165). And with N equal to 3, there is the intriguing possibility that the stable configurations could be conceived as resembling the organization of sets of electron orbits around an atom. Such "atoms" might lend themselves to a Mendeleyev-type periodic classification into what would then be a (developmental) sequence of viable "learning manifolds", each with characteristics properties, whether as a description of a multi-facetted personality, group, or society.